Many subjects require the teaching of abstractions. Often these abstractions are represented using specialized symbols. From the simplest beginnings of arithmetic, where numbers and letters are the abstract symbols we use, to the most advanced mathematics, such symbols pervade our culture. The letters of the alphabet are the first symbols we learn, and are the building blocks of our written language.
In the process of teaching various subjects, these symbols are used to create meaningful expressions. These expressions are often transformed into other expressions, for simplification or illustration purposes, according to some rules. In the subject of mathematics, a linear algebraic equation with one unknown is an example of a symbolic expression, and the steps needed for its solution are the symbolic transformations of the original equation.
Chemical formulas are another example of symbolic representations, where the transformations may represent chemical reactions, ionic dissociations, or changes of crystal structure, many of which can be illustrated with more concrete diagrammatic models.
The transformations of words in linguistics are the declensions of nouns, conjugations of verbs, changes of characters within words to correct spelling, and changes of word order in sentences to change meaning or illustrate different meanings. These in turn can be illustrated with the linguistic meaning of each.
Although many software programs have been developed to help in the instruction of such subjects, they all present the transformations in discrete steps. The actual transformations have to be inferred from the starting expression followed by the transformed, ending one. Such inference is sometimes difficult for some people to make and requires a visualization of the continuous process.
For example, the conventional method of illustrating how a mathematical expression is transformed, is to display each step, in a step-by-step process, leaving the previous expression displayed, so the viewer can compare it with the current one and thus deduce the details of the transformation. Unfortunately, many viewers find it difficult to make that deduction, even when this is explained, and this frustrates their understanding.
When a human presenter, as opposed to a computer program, makes presentations, he or she will often point to various parts of the expression while explaining the transformation process. Additionally, a human presenter can be asked questions if the presentation is not clear.
By highlighting and animating, in a continuous fashion, the transformation of an expression, a computer program can improve on, and also enhance, human presentations of such abstract material. Animations will have the additional advantage of helping pictorially oriented users to visualize the transformation rules and thus aid in their memorization and understanding.
Any tool which helps visualize and make concrete the abstract rules governing expression transformations, will also be useful in presentations, both in education and in other professional situations.
Simple concrete model analogies of abstract representations are sometimes used in textbooks. When such models can be dynamically tied to the abstract expressions, the result can be a very powerful concrete dynamic model of the underlying abstract system. Transformations of the symbolic representations are immediately reflected as concrete changes in the pictorial concrete model, making the rules governing these transformations intuitive and almost obvious.